Least Common Multiple of 30000 and 30004

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 30000 and 30004 the smallest integer that is 225030000 that is divisible by both numbers.

Least Common Multiple (LCM) of 30000 and 30004 is 225030000.

LCM(30000,30004) = 225030000

LCM of 30000 and 30004

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 30000 and 30004

LCM of 30000 and 30004 is 225030000

Least common multiple can be found by multiplying the highest exponent prime factors of 30000 and 30004. First we will calculate the prime factors of 30000 and 30004.

Prime Factorization of 30000


2 30000
2 15000
2 7500
2 3750
3 1875
5 625
5 125
5 25
5 5
1

Prime factors of 30000 are 2, 3,5. Prime factorization of 30000 in exponential form is:

30000 = 24×31×54

Prime Factorization of 30004


2 30004
2 15002
13 7501
577 577
1

Prime factors of 30004 are 2, 13,577. Prime factorization of 30004 in exponential form is:

30004 = 22×131×5771

Now multiplying the highest exponent prime factors to calculate the LCM of 30000 and 30004.

LCM(30000,30004) = 24×31×54×131×5771
LCM(30000,30004) = 225030000

Factors of 30000

List of positive integer factors of 30000 that divides 30000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 625, 750, 1000, 1200, 1250, 1500, 1875, 2000, 2500, 3000, 3750, 5000, 6000, 7500, 10000, 15000, 30000

Factors of 30004

List of positive integer factors of 30004 that divides 30004 without a remainder.

1, 2, 4, 13, 26, 52, 577, 1154, 2308, 7501, 15002, 30004

Least Common Multiple of 30000 and 30004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30000 and 30004, than apply into the LCM equation.

GCF(30000,30004) = 4
LCM(30000,30004) = ( 30000 × 30004) / 4
LCM(30000,30004) = 900120000 / 4
LCM(30000,30004) = 225030000

Properties of LCM 30000 and 30004

(i) The LCM of 30004 and 30000 is associative

LCM of 30000 and 30004 = LCM of 30004 and 30000

Related Least Common Multiples of 30000

Related Least Common Multiples of 30004

Frequently Asked Questions on LCM of 30000 and 30004

1. What is the LCM of 30000 and 30004?

Answer: LCM of 30000 and 30004 is 225030000.

2. What are the Factors of 30000?

Answer: Factors of 30000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 625, 750, 1000, 1200, 1250, 1500, 1875, 2000, 2500, 3000, 3750, 5000, 6000, 7500, 10000, 15000, 30000. There are 50 integers that are factors of 30000. The greatest factor of 30000 is 30000.

3. What are the Factors of 30004?

Answer: Factors of 30004 are 1, 2, 4, 13, 26, 52, 577, 1154, 2308, 7501, 15002, 30004. There are 12 integers that are factors of 30004. The greatest factor of 30004 is 30004.

4. How to Find the LCM of 30000 and 30004?

Answer:

Least Common Multiple of 30000 and 30004 = 225030000

Step 1: Find the prime factorization of 30000

30000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5

Step 2: Find the prime factorization of 30004

30004 = 2 x 2 x 13 x 577

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 225030000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5 x 13 x 577

Step 4: Therefore, the least common multiple of 30000 and 30004 is 225030000.